Question

In an atom two electrons move around the nucleus in circular orbit of radii R and 4R. The ratio of time taken by them to complete one revolution is
(a)1:8 (b)4:1 (c)1:4 (d)8:7

Answer 1

Answer:

1 : 8

Explanation:

Given In an atom two electrons move around the nucleus in circular orbit of radii R and 4R. The ratio of time taken by them to complete one revolution is

Given v is proportional to 1/√r

          v ∝ 1/√r

      So v a ∝ 1/√r

         vb ∝  1/√4 r

      va / vb = 2

Now ta / tb = 2πr / va / 2 π (4 r) / vb

         = vb / 4 va

         = 1/4 x vb / va

       = 1/4 x 1/2  

        = 1/8

       = 1 : 8

The ratio of time taken by them to complete one revolution is 1:8

Answer 2

Answer:

1:8

Explanation:

Given:- R1=R and R2=4R

We know that

T=R^3/2

So

T1:T2=(R1:R2)^3/2

T1:T2=(R:4R)^3/2

T1:T2=(1:4)^3/2

T1:T2=1:8